Theoretical Biology – serie

This book covers recent developments in epidemic process models and related data on temporally varying networks. It is widely recognized that contact networks are indispensable for describing, understanding, and intervening to stop the spread of infectious diseases in human and animal populations; “network epidemiology” is an umbrella term to describe this research field.More recently, contact networks have been recognized as being highly dynamic. This observation, also supported by an increasing amount of new data, has led to research on temporal networks, a rapidly growing area. Changes in network structure are often informed by epidemic (or other) dynamics, in which case they are referred to as adaptive networks.This volume gathers contributions by prominent authors working in temporal and adaptive network epidemiology, a field essential to understanding infectious diseases in real society.

This book covers recent developments in epidemic process models and related data on temporally varying networks. It is widely recognized that contact networks are indispensable for describing, understanding, and intervening to stop the spread of infectious diseases in human and animal populations; “network epidemiology” is an umbrella term to describe this research field.More recently, contact networks have been recognized as being highly dynamic. This observation, also supported by an increasing amount of new data, has led to research on temporal networks, a rapidly growing area. Changes in network structure are often informed by epidemic (or other) dynamics, in which case they are referred to as adaptive networks.This volume gathers contributions by prominent authors working in temporal and adaptive network epidemiology, a field essential to understanding infectious diseases in real society.

This book presents a unique fusion of two different research topics. One is related to the traditional mathematical problem of chases and escapes. The problem mainly deals with a situation where a chaser pursues an evader to analyze their trajectories and capture time. It dates back more than 300 years and has developed in various directions such as differential games. The other topic is the recently developing field of collective behavior, which investigates origins and properties of emergent behavior in groups of self-driving units. Applications include schools of fish, flocks of birds, and traffic jams. This book first reviews representative topics, both old and new, from these two areas. Then it presents the combined research topic of "group chase and escape", recently proposed by the authors. Although the combination is simple and straightforward, the book describes the emergence of rather intricate behavior, provoking the interest of readers for further developments and applications of related topics.

This book presents a unique fusion of two different research topics. One is related to the traditional mathematical problem of chases and escapes. The problem mainly deals with a situation where a chaser pursues an evader to analyze their trajectories and capture time. It dates back more than 300 years and has developed in various directions such as differential games. The other topic is the recently developing field of collective behavior, which investigates origins and properties of emergent behavior in groups of self-driving units. Applications include schools of fish, flocks of birds, and traffic jams. This book first reviews representative topics, both old and new, from these two areas. Then it presents the combined research topic of "group chase and escape", recently proposed by the authors. Although the combination is simple and straightforward, the book describes the emergence of rather intricate behavior, provoking the interest of readers for further developments and applications of related topics.

This book presents new theoretical perspectives on ecological community dynamics and in so doing casts fresh light on the enduring complexity–stability debate. Real ecological communities do not simply comprise diverse species and interactions, which respectively represented the nodes and links of the classic network theory. Rather, they are characterized by different types of complexity, and this book explains how this diversity of complexity is key to understanding the dynamics of ecological communities. It is shown how various properties in natural communities, such as life history, adaptation, density dependence, sex, interaction types, space, functional traits, and microbial processes, can dramatically increase the complexity in ecological communities. Furthermore, innovative methods are introduced that may be applied to cast light on very complex communities. With each chapter presenting the latest advances and approaches, the book sets the direction for future researchon ecological community dynamics. It will be a “must read” for researchers and students in the field of ecology.

This book presents new theoretical perspectives on ecological community dynamics and in so doing casts fresh light on the enduring complexity–stability debate. Real ecological communities do not simply comprise diverse species and interactions, which respectively represented the nodes and links of the classic network theory. Rather, they are characterized by different types of complexity, and this book explains how this diversity of complexity is key to understanding the dynamics of ecological communities. It is shown how various properties in natural communities, such as life history, adaptation, density dependence, sex, interaction types, space, functional traits, and microbial processes, can dramatically increase the complexity in ecological communities. Furthermore, innovative methods are introduced that may be applied to cast light on very complex communities. With each chapter presenting the latest advances and approaches, the book sets the direction for future researchon ecological community dynamics. It will be a “must read” for researchers and students in the field of ecology.

This book describes the dynamics of biological cells and their mathematical modeling. The topics cover the dynamics of RNA polymerases in transcription, construction of vascular networks in angiogenesis, and synchronization of cardiomyocytes. Statistical analysis of single cell dynamics and classification of proteins by mathematical modeling are also presented. The book provides the most up-to-date information on both experimental results and mathematical models that can be used to analyze cellular dynamics. Novel experimental results and approaches to understand them will be appealing to the readers. Each chapter contains 1) an introductory description of the phenomenon, 2) explanations about the mathematical technique to analyze it, 3) new experimental results, 4) mathematical modeling and its application to the phenomenon. Elementary introductions for the biological phenomenon and mathematical approach to them are especially useful for beginners.The importance of collaboration between mathematics and biological sciences has been increasing and providing new outcomes. This book gives good examples of the fruitful collaboration between mathematics and biological sciences.

This book describes the dynamics of biological cells and their mathematical modeling. The topics cover the dynamics of RNA polymerases in transcription, construction of vascular networks in angiogenesis, and synchronization of cardiomyocytes. Statistical analysis of single cell dynamics and classification of proteins by mathematical modeling are also presented. The book provides the most up-to-date information on both experimental results and mathematical models that can be used to analyze cellular dynamics. Novel experimental results and approaches to understand them will be appealing to the readers. Each chapter contains 1) an introductory description of the phenomenon, 2) explanations about the mathematical technique to analyze it, 3) new experimental results, 4) mathematical modeling and its application to the phenomenon. Elementary introductions for the biological phenomenon and mathematical approach to them are especially useful for beginners.The importance of collaboration between mathematics and biological sciences has been increasing and providing new outcomes. This book gives good examples of the fruitful collaboration between mathematics and biological sciences.

This book describes the shape formation of living organisms using mathematical models. Genes are deeply related to the shape of living organisms, and elucidation of a pathway of shape formation from genes is one of the fundamental problems in biology. Mathematical cell models are indispensable tools to elucidate this problem.  The book introduces two mathematical cell models, the cell center model and the vertex model, with their applications. The cell center model is applied to elucidate the formation of neat cell arrangements in epidermis, cell patterns consisting of heterogeneous-sized cells, capillary networks, and the branching patterns of blood vessels. The vertex model is applied to elucidate the wound healing mechanisms of the epithelium and ordered pattern formation involving apoptosis. Pattern formation with differential cell adhesion is also described. The vertex model is then extended from a two-dimensional (2D) to a three-dimensional (3D) model. A cell aggregate involving a large cavity is described to explain the development of the mammalian blastocyst or the formation of an epithelial vesicle. Epithelial tissues and the polarity formation process of the epithelium are also explained. The vertex model also recapitulates active remodeling of tissues and describes the twisting of tissue that contributes to understanding the cardiac loop formation of the embryonic tube. The book showcases that mathematical cell models are indispensable tools to understand the shape formation of living organisms. Successful contribution of the mathematical cell models means that the remodeling of collective cells is self-construction. Examining the successive iterations of self-constructions leads to understanding the remarkable and mysterious morphogenesis that occurs during the development of living organisms.  The intended readers of this book are not only theoretical or mathematical biologists, but also experimental andgeneral biologists, including undergraduate and postgraduate students who are interested in the relationship between genes and morphogenesis.

This book describes the shape formation of living organisms using mathematical models. Genes are deeply related to the shape of living organisms, and elucidation of a pathway of shape formation from genes is one of the fundamental problems in biology. Mathematical cell models are indispensable tools to elucidate this problem.  The book introduces two mathematical cell models, the cell center model and the vertex model, with their applications. The cell center model is applied to elucidate the formation of neat cell arrangements in epidermis, cell patterns consisting of heterogeneous-sized cells, capillary networks, and the branching patterns of blood vessels. The vertex model is applied to elucidate the wound healing mechanisms of the epithelium and ordered pattern formation involving apoptosis. Pattern formation with differential cell adhesion is also described. The vertex model is then extended from a two-dimensional (2D) to a three-dimensional (3D) model. A cell aggregate involving a large cavity is described to explain the development of the mammalian blastocyst or the formation of an epithelial vesicle. Epithelial tissues and the polarity formation process of the epithelium are also explained. The vertex model also recapitulates active remodeling of tissues and describes the twisting of tissue that contributes to understanding the cardiac loop formation of the embryonic tube. The book showcases that mathematical cell models are indispensable tools to understand the shape formation of living organisms. Successful contribution of the mathematical cell models means that the remodeling of collective cells is self-construction. Examining the successive iterations of self-constructions leads to understanding the remarkable and mysterious morphogenesis that occurs during the development of living organisms.  The intended readers of this book are not only theoretical or mathematical biologists, but also experimental andgeneral biologists, including undergraduate and postgraduate students who are interested in the relationship between genes and morphogenesis.

This book shows that evolutionary game theory can unravel how mutual cooperation, trust, and credit in a group emerge in organizations and institutions. Some organizations and institutions, such as insurance unions, credit unions, and banks, originated from very simple mutual-aid groups. Members in these early-stage mutual-aid groups help each other, making rules to promote cooperation, and suppressing free riders. Then, they come to “trust” not only each other but also the group they belong to, itself. The division of labor occurs when the society comes to have diversity and complexity in a larger group, and the division of labor also requires mutual cooperation and trust among different social roles. In a larger group, people cannot directly interact with each other, and the reputation of  unknown people helps other decide who is a trustworthy person. However, if gossip spreads untruths about a reputation, trust and cooperation are destroyed.Therefore, how to suppress untrue gossip is also important for trust and cooperation in a larger group. If trustworthiness and credibility can be established, these groups are successfully sustainable. Some develop and evolve and then mature into larger organizations and institutions. Finally, these organizations and institutions become what they are now. Therefore, not only cooperation but also trust and credit are keys to understanding these organizations and institutions.The evolution of cooperation, a topic of research in evolutionary ecology and evolutionary game theory, can be applied to understanding how to make institutions and organizations sustainable, trustworthy, and credible. It provides us with the idea that evolutionary game theory is a good mathematical tool to analyze trust and credit. This kind of research can be applied to current hot topics such as microfinance and the sustainable use of ecosystems.

This book shows that evolutionary game theory can unravel how mutual cooperation, trust, and credit in a group emerge in organizations and institutions. Some organizations and institutions, such as insurance unions, credit unions, and banks, originated from very simple mutual-aid groups. Members in these early-stage mutual-aid groups help each other, making rules to promote cooperation, and suppressing free riders. Then, they come to “trust” not only each other but also the group they belong to, itself. The division of labor occurs when the society comes to have diversity and complexity in a larger group, and the division of labor also requires mutual cooperation and trust among different social roles. In a larger group, people cannot directly interact with each other, and the reputation of  unknown people helps other decide who is a trustworthy person. However, if gossip spreads untruths about a reputation, trust and cooperation are destroyed.Therefore, how to suppress untrue gossip is also important for trust and cooperation in a larger group. If trustworthiness and credibility can be established, these groups are successfully sustainable. Some develop and evolve and then mature into larger organizations and institutions. Finally, these organizations and institutions become what they are now. Therefore, not only cooperation but also trust and credit are keys to understanding these organizations and institutions.The evolution of cooperation, a topic of research in evolutionary ecology and evolutionary game theory, can be applied to understanding how to make institutions and organizations sustainable, trustworthy, and credible. It provides us with the idea that evolutionary game theory is a good mathematical tool to analyze trust and credit. This kind of research can be applied to current hot topics such as microfinance and the sustainable use of ecosystems.

This textbook provides an introduction to the mathematical models of population dynamics in mathematical biology. The focus of this book is on the biological meaning/translation of mathematical structures in mathematical models, rather than simply explaining mathematical details and literacies to analyze a model. In some recent usages of the mathematical model simply with computer numerical calculations, the model includes some inappropriate mathematical structure concerning the reasonability of modeling for the biological problem under investigation. For students and researchers who study or use mathematical models, it is important and helpful to understand what mathematical setup could be regarded as reasonable for the model with respect to the relation between the biological factors involved in the assumptions and the mathematical structure of the model.Topics covered in this book are; modeling with geometric progression, density effect in population dynamics, deriving continuous time models from discrete time models, basic modeling for birth-death stochastic processes, continuous time models, modeling interspecific reaction for the continuous time population dynamics model, competition and prey-predator dynamics, modeling for population dynamics with a heterogeneous structure of population, qualitative analysis on the discrete time dynamical system, necessary knowledge about fundamental mathematical theories to understand the dynamical nature of continuous time models. The book includes popular topics in ecology and mathematical biology, as well as classic theoretical topics.By understanding the biological meaning of modeling for simple models, readers will be able to derive a specific mathematical model for a biological problem by reasonable modeling. The contents of this book is made accessible for readers without strong Mathematical background.

This textbook provides an introduction to the mathematical models of population dynamics in mathematical biology. The focus of this book is on the biological meaning/translation of mathematical structures in mathematical models, rather than simply explaining mathematical details and literacies to analyze a model. In some recent usages of the mathematical model simply with computer numerical calculations, the model includes some inappropriate mathematical structure concerning the reasonability of modeling for the biological problem under investigation. For students and researchers who study or use mathematical models, it is important and helpful to understand what mathematical setup could be regarded as reasonable for the model with respect to the relation between the biological factors involved in the assumptions and the mathematical structure of the model.Topics covered in this book are; modeling with geometric progression, density effect in population dynamics, deriving continuous time models from discrete time models, basic modeling for birth-death stochastic processes, continuous time models, modeling interspecific reaction for the continuous time population dynamics model, competition and prey-predator dynamics, modeling for population dynamics with a heterogeneous structure of population, qualitative analysis on the discrete time dynamical system, necessary knowledge about fundamental mathematical theories to understand the dynamical nature of continuous time models. The book includes popular topics in ecology and mathematical biology, as well as classic theoretical topics.By understanding the biological meaning of modeling for simple models, readers will be able to derive a specific mathematical model for a biological problem by reasonable modeling. The contents of this book is made accessible for readers without strong Mathematical background.

This book helps the reader make use of the mathematical models of biological phenomena starting from the basics of programming and computer simulation. Computer simulations based on a mathematical model enable us to find a novel biological mechanism and predict an unknown biological phenomenon. Mathematical biology could further expand the progress of modern life sciences. Although many biologists are interested in mathematical biology, they do not have experience in mathematics and computer science. An educational course that combines biology, mathematics, and computer science is very rare to date. Published books for mathematical biology usually explain the theories of established mathematical models, but they do not provide a practical explanation for how to solve the differential equations included in the models, or to establish such a model that fits with a phenomenon of interest. MATLAB is an ideal programming platform for the beginners of computer science. This book starts from the very basics about how to write a programming code for MATLAB (or Octave), explains how to solve ordinary and partial differential equations, and how to apply mathematical models to various biological phenomena such as diabetes, infectious diseases, and heartbeats. Some of them are original models, newly developed for this book. Because MATLAB codes are embedded and explained throughout the book, it will be easy to catch up with the text. In the final chapter, the book focuses on the mathematical model of the proneural wave, a phenomenon that guarantees the sequential differentiation of neurons in the brain. This model was published as a paper from the author’s lab (Sato et al., PNAS 113, E5153, 2016), and was intensively explained in the book chapter “Notch Signaling in Embryology and Cancer”, published by Springer in 2020. This book provides the reader who has a biological background with invaluable opportunities to learn and practice mathematical biology.

This book helps the reader make use of the mathematical models of biological phenomena starting from the basics of programming and computer simulation. Computer simulations based on a mathematical model enable us to find a novel biological mechanism and predict an unknown biological phenomenon. Mathematical biology could further expand the progress of modern life sciences. Although many biologists are interested in mathematical biology, they do not have experience in mathematics and computer science. An educational course that combines biology, mathematics, and computer science is very rare to date. Published books for mathematical biology usually explain the theories of established mathematical models, but they do not provide a practical explanation for how to solve the differential equations included in the models, or to establish such a model that fits with a phenomenon of interest. MATLAB is an ideal programming platform for the beginners of computer science. This book starts from the very basics about how to write a programming code for MATLAB (or Octave), explains how to solve ordinary and partial differential equations, and how to apply mathematical models to various biological phenomena such as diabetes, infectious diseases, and heartbeats. Some of them are original models, newly developed for this book. Because MATLAB codes are embedded and explained throughout the book, it will be easy to catch up with the text. In the final chapter, the book focuses on the mathematical model of the proneural wave, a phenomenon that guarantees the sequential differentiation of neurons in the brain. This model was published as a paper from the author’s lab (Sato et al., PNAS 113, E5153, 2016), and was intensively explained in the book chapter “Notch Signaling in Embryology and Cancer”, published by Springer in 2020. This book provides the reader who has a biological background with invaluable opportunities to learn and practice mathematical biology.

This open access book presents a multidisciplinary examination of how biological shapes, structures, and dynamic patterns emerge, evolve, and persist in the natural world. Drawing on genetics, developmental biology, evolutionary theory, physics, chemistry, and mathematical modeling, the book brings together leading researchers who illuminate the fundamental principles behind the diversity of forms found in living organisms.The chapters span a wide scientific landscape. Readers encounter discussions of symmetry breaking from physics to biology, models of collective cell behavior, and the mechanisms and evolutionary history of female-limited Batesian mimicry in Papilio butterflies. The volume also includes mathematical and computational analyses of pattern formation and population dynamics, as well as investigations into the development and evolution of butterfly wing patterns. Additional chapters examine how a single gene can determine snail coiling direction, explore morphospace approaches to evolution, and analyze the functional morphology of molluscan shells. Other contributions reveal the mechanical optimality embedded in plant structures and highlight striking spiral patterns and morphologies found in chemical systems.Based on invited lectures delivered at the 6th Yamada Symposium in Tokyo, this book provides readers with an integrated view of pattern formation across scales and disciplines. It serves as an engaging guide for researchers, students, and anyone interested in understanding how nature generates its remarkable variety of forms.

This textbook introduces essential mathematical concepts and techniques through concrete examples for those studying biology and related fields. It aims to convey the fascination of using mathematical models to understand living systems while providing the foundational skills needed to analyze such models.In recent years, mathematical modeling has become increasingly important for understanding biological phenomena. Such models now play crucial roles in fields ranging from neuronal electrical activity and the molecular mechanisms of muscle contraction to the formation of morphological patterns during development and the study of brain function. Advances in modeling ecological and social behavior, as well as evolutionary processes, have further established mathematical modeling as an indispensable tool in theoretical and mathematical biology.Mathematical models clarify logical structures, uncover unexpected patterns, and reveal commonalities across seemingly different disciplines. They also enable quantitative predictions that allow hypotheses to be tested against experimental and observational data.Chapters in this book cover topics such as population dynamics, adaptive strategies, and principles of coexistence. Readers are introduced to dynamic optimization, control theory, and game theory, along with stochastic modeling techniques based on Markov and diffusion processes.The purpose of this book is to present mathematical ideas in an intuitive and accessible way, helping biology students appreciate the fascination of mathematical modeling while acquiring essential analytical skills. With a focus on ecological contexts, it provides the background knowledge and core concepts needed to show how simple models can clarify underlying logic and unify diverse biological phenomena.

This textbook provides an introduction to theoretical biology using specific topics and explains the main mathematical methods. The book also introduces the “structural theories” developed by the author and his colleagues as new theoretical methods. Structural theories are mathematical theories that determine key aspects of the behavior of dynamical systems from network information alone. The book details the practical applications of these methods across several biological network systems and shows that they are practically useful for analyzing the behaviors of biological systems.The first half of the book focuses on the dynamics that arise from the regulation of biomolecular activity, such as gene expression and protein modification. The second half of the book approaches the understanding of the dynamics of complex systems composed of many biomolecules. Each chapter covers current and important topics in biological research, and its description of how biological phenomena are theoretically elucidated effectively conveys the importance and appeal of mathematical methods.This book is not only a comprehensive textbook on theoretical biology, but also a study guide for learning mathematical methods. It also serves as a specialized reference for systematically learning new mathematical theories. The “Mathematical Methods” section at the end of each chapter offers a concise summary and facilitates efficient learning for readers, along with the exercises. Target readers of this book are from upper undergraduate students to senior researchers interested in the dynamics of complex network systems in biology. It appeals to both mathematical and experimental biologists, as well as chemists and physicists.

This book introduces various mathematical models used in ecological risk assessment, primarily discussing models used in hazard assessment. The book aims to link ecology and conservation biology with risk assessments, bringing together the knowledge of ecotoxicology and ecology for effective risk assessment. The first part describes population-level assessment in ecological risk assessment. The chapters cover current methodologies for ecological risk assessment, individual-level assessment, population dynamics models for population-level assessment, case studies, mathematical models for population extinctions, the derivation of mean time to extinction (MTE) and their case studies. The second part of the book discusses the mathematical models involved in hazard assessments. It introduces the method of risk assessment using species sensitivity distributions (SSDs), hazard assessment of metals, chemical mixtures using the Michaelis-Menten equation, basic elements of statistics and related topics. Expected readers are risk assessors in governments and public sectors, students and young researchers interested in environmental science. The book is made accessible and easy to follow by beginners in mathematical biology and theoretical ecology.